Question: Solve for $k$, $ -\dfrac{6}{15k} = -\dfrac{5k - 9}{20k} - \dfrac{6}{5k} $
Solution: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $15k$ $20k$ and $5k$ The common denominator is $60k$ To get $60k$ in the denominator of the first term, multiply it by $\frac{4}{4}$ $ -\dfrac{6}{15k} \times \dfrac{4}{4} = -\dfrac{24}{60k} $ To get $60k$ in the denominator of the second term, multiply it by $\frac{3}{3}$ $ -\dfrac{5k - 9}{20k} \times \dfrac{3}{3} = -\dfrac{15k - 27}{60k} $ To get $60k$ in the denominator of the third term, multiply it by $\frac{12}{12}$ $ -\dfrac{6}{5k} \times \dfrac{12}{12} = -\dfrac{72}{60k} $ This give us: $ -\dfrac{24}{60k} = -\dfrac{15k - 27}{60k} - \dfrac{72}{60k} $ If we multiply both sides of the equation by $60k$ , we get: $ -24 = -15k + 27 - 72$ $ -24 = -15k - 45$ $ 21 = -15k $ $ k = -\dfrac{7}{5}$